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anonymous

  • one year ago

Find the greatest 4 digits number which when divided by 18,24,30 and 36 leaves a remainder 17 (in each case).

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  1. amoodarya
    • one year ago
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    a=18q+17 a=24k+17 a=30p+17 so 30|a-17 24|a-17 18|a-17 so [24,18,30]|a-17

  2. anonymous
    • one year ago
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    I need a way by which I can calculate answer to such question in 1-2 mins time. This type of questions appears in admission exam for MS(CS).

  3. anonymous
    • one year ago
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    no offense but @amoodarya I got no clue what you did back there. A little explanation please ?

  4. UsukiDoll
    • one year ago
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    that notation for the second one is 30 divides a -17 similarly 24 divides a-17 and 18 divides 1-17

  5. ganeshie8
    • one year ago
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    Let \(a\) = required number Notice that \(a-17\) is divisible by each of the given integers, therefore \(a-17\) must also be divisible by their lcm, \(360\) : \[a-17 = 360k\]

  6. amoodarya
    • one year ago
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    [30,24,18]=[5.3.2, 2.2.2.3, 3.3.2]=2.2.2.3.3.5=\[2^3*3^2*5=360\\a-17=360k\\a=360k+17\\a_\min=360*3+17=1080+17\]

  7. anonymous
    • one year ago
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    @ganeshie8 and others thank you!

  8. UsukiDoll
    • one year ago
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    when did k =3 for the last line? just wondering. unless we have k = 3 because it's the lcm of 18,24,30, and 36.

  9. anonymous
    • one year ago
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    Lol I think @amoodarya assumed k = 3 :P

  10. UsukiDoll
    • one year ago
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    :S there is always a reason to let k = 3. isn't it?

  11. anonymous
    • one year ago
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    I can't think of any reasons to do so :| cause 3 isn't given in the question

  12. UsukiDoll
    • one year ago
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    the only thing I can think of is that 3 is the lcm of 18.24.30.36.. not to mention that's part of the 3 x table 3 x 6 =18 3 x 8 = 24 3 x 10 = 30 3 x 12 = 36 3 x 3 x 2 = 18 3 x 2 x 2 x 2 = 24 3 x 2 x 5 = 30 3 x 3 x 2 x 2 Each of them has at least 1 3

  13. anonymous
    • one year ago
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    yup thats true

  14. anonymous
    • one year ago
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    @amoodarya it'll be less confusing if you just type down a few words explaining the problem like ganeshie8 did. Thanks

  15. amoodarya
    • one year ago
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    \[a=360k+17 \ge 1000\\360k \ge 1000-17\\k \ge \frac{1000-17}{360}\\k \space is \space integer \\k \ge 3\]

  16. UsukiDoll
    • one year ago
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    where did you get the 1000 from?

  17. anonymous
    • one year ago
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    largest 4 digit number is 9999 Man Imma cry now seriously

  18. anonymous
    • one year ago
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    @amoodarya you're not helping sir rather you are making it more confusing and complex :|

  19. UsukiDoll
    • one year ago
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    yeah this is how my adviser would do... just be like ok this this this the end.

  20. anonymous
    • one year ago
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    LOL I hate such kind of teachers >:| Teacher's job is to explain the whole process....

  21. UsukiDoll
    • one year ago
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    yeah I got a B- for absolutely knowing 5.5 out of 8 chapters in Passage to Advanced Mathematics book

  22. amoodarya
    • one year ago
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    oh . sorry i had a little mistake i wrote it for smallest 4 digits so you do it for the greatest , like that

  23. anonymous
    • one year ago
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    @ganeshie8 can you make things simple its seriously frying my brain :|

  24. UsukiDoll
    • one year ago
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    wow I wish my retired professor was on here. He was awesome.

  25. ganeshie8
    • one year ago
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    spoonfeeding is not good always, it would be more fun if you try and solve the problem on your own based on the given hints

  26. amoodarya
    • one year ago
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    \[a \leq 9999\\360k+17 \leq 9999\\k \leq \frac{9999-17}{360}\]

  27. UsukiDoll
    • one year ago
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    well what if the person made so many attempts and then got fed up?

  28. ganeshie8
    • one year ago
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    where are the "many" attempts ?

  29. anonymous
    • one year ago
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    ^ yes that's what I am doing for last 1 hour :|

  30. UsukiDoll
    • one year ago
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    k is less than or equal to 27.7222222222 something seems legit

  31. UsukiDoll
    • one year ago
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    "many" attempts? lol like using every theorem out there

  32. ganeshie8
    • one year ago
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    teaching is not easy... there is no way for a teacher to know what the student has already tried right

  33. UsukiDoll
    • one year ago
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    showing off like what my professor did to me a while back doesn't help me understand either -_-

  34. anonymous
    • one year ago
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    ^

  35. ganeshie8
    • one year ago
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    try this : teach me how to multiply 3*5

  36. UsukiDoll
    • one year ago
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    ummm let's see. it's like writing 3 5 times and adding them up

  37. anonymous
    • one year ago
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    3*5 = 15 simple enough :O

  38. ganeshie8
    • one year ago
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    how do you know i know addition ?

  39. UsukiDoll
    • one year ago
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    omg! take 3 rocks that's 1 batch then 3 rocks 3 rocks 3 rocks 3 rocks... add them all up

  40. anonymous
    • one year ago
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    alright I'll solve it myself .... no more arguments

  41. ganeshie8
    • one year ago
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    where do i find rocks ? your explanation is confusing me

  42. UsukiDoll
    • one year ago
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    you find rocks outside!

  43. amoodarya
    • one year ago
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    |dw:1435484624755:dw|

  44. UsukiDoll
    • one year ago
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    or buy them or find them at a park or at your house

  45. ganeshie8
    • one year ago
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    now that i don't want to buy rocks, why do i need rocks ? how are they related to multiplications

  46. anonymous
    • one year ago
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    OMG thats childish @ganeshie8 :| @amoodarya 's work was confusing me because he took the question wrongly.

  47. UsukiDoll
    • one year ago
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    don't want to buy rocks ! BORROW MARBLES FROM YOUR FRIEND!

  48. anonymous
    • one year ago
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    I'm outta here seriously....

  49. ganeshie8
    • one year ago
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    so i need to have a friend to understand multiplcations ?

  50. UsukiDoll
    • one year ago
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    -_-! you have none.. draw circles on paper.

  51. ganeshie8
    • one year ago
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    Okay enough, we're not getting anywhere. I hate math and you're the reason for that.

  52. UsukiDoll
    • one year ago
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    wow... then you as a student fail then

  53. ganeshie8
    • one year ago
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    isn't that obvious

  54. UsukiDoll
    • one year ago
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    *rolls eyes* why waste my time with gibberish? If you still don't understand it after so many tries, it becomes useless to the point that the only way to solve this issue to just fail the student and send it to summer school.

  55. ganeshie8
    • one year ago
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    same thing can repeat in summer school

  56. UsukiDoll
    • one year ago
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    then why should the student still be in school then? Have it kicked out of the system and force it to get a job.

  57. ganeshie8
    • one year ago
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    more or less, thats the story of most school dropout these days right one bad/annoying teacher is all it takes

  58. UsukiDoll
    • one year ago
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    not the teacher's fault really. It's the student. If they are not committed...don't bother... just do something productive with life and that's it.

  59. ganeshie8
    • one year ago
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    you(teacher) failed to teach me(3rd grade kid) how to multiply

  60. UsukiDoll
    • one year ago
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    -_-! No you failed yourself.

  61. ganeshie8
    • one year ago
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    more than that, you killed my confidence and love of math

  62. UsukiDoll
    • one year ago
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    and you have gotten really annoying after a while.

  63. ganeshie8
    • one year ago
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    hmm

  64. UsukiDoll
    • one year ago
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    annas and amoodarya got it right. It was just you !

  65. ganeshie8
    • one year ago
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    aren't we role modeling anymore, you as a good teacher and me as a poor student ?

  66. UsukiDoll
    • one year ago
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    KNOCK IT OFF ALREADY!

  67. ganeshie8
    • one year ago
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    Okay fine

  68. UsukiDoll
    • one year ago
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    and it's role playing...

  69. anonymous
    • one year ago
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    It's a fault on both ends cause our teachers now a days are not as determined as they used to be in 90's and our students shows no seriousness in studies. Well it is kind of a fault of teachers, a good teacher always try to develop interest of his/her students in the subject. Our education system is faulty and teacher's only see teaching as a profession and nothing else.... Sad story!

  70. UsukiDoll
    • one year ago
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    geez... this is not helping annas at ALL! What started out as trying to clarify things turned into stupid stuff that is NONSENSE AND OFF TOPIC!

  71. ganeshie8
    • one year ago
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    I agree annas, its always the fault of teacher.

  72. UsukiDoll
    • one year ago
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    what about favoritism?

  73. anonymous
    • one year ago
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    @ganeshie8 I am not a 2 year old to be spoon feed I know maths very well... Only problem is I dont remember basic stuff cause of lack of practice. And I am doing this basic stuff just for a stupid test for admission in MS. I've an interview related to my field i.e. software engineering but to qualify for that I need to clear this stupid test... The only reason to ask this question...

  74. UsukiDoll
    • one year ago
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    that's it... @Michele_Laino Help :*(

  75. anonymous
    • one year ago
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    Favoritism is another issue in our education system... Teachers give marks for free to those students that they think are most favorite... It's a flaw of teacher AGAIN. I hate this current education system.

  76. ganeshie8
    • one year ago
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    i think we're done with the original main q ?

  77. anonymous
    • one year ago
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    Oh I solved the question on my own thank you @UsukiDoll answer I got was 9989. @ganeshie8 I didnt start all this discussion all I was asking is for some clarification.

  78. ganeshie8
    • one year ago
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    9989 is wrong are you still looking for clarification ? what part do you not understand in ammodarya's solution ?

  79. UsukiDoll
    • one year ago
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    @annas I know a good example that happened at my university remembered that annoying professor I had for that Intro to Advanced Mathematics class? he gave me a B- which was surprising because like I said I only mastered 5.5 out of 8 chapters. Fast forward to a year later... some girl had the same professor and ended up almost failing like a D- Keep in mind that annoying professor happens to be my undergrad. adviser.

  80. ganeshie8
    • one year ago
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    \(a = 360k+17\) Is it hard to solve \(k\) that gives the maximum \(4\) digit number ?

  81. anonymous
    • one year ago
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    I was taking k = 27.7 now I took k = 27 and I got 9737

  82. ganeshie8
    • one year ago
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    thats looks correct

  83. anonymous
    • one year ago
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    Alright, thanks

  84. ganeshie8
    • one year ago
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    yw, the dicussion was not so fruitful but i enjoyed it thanks!

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